caveat to the below: I have extra 328P-PU's and my Uno's have sockets. That plus know-how cuts the cost of mistakes deeply.
Oh, you might like this, I connected the IRLZ44N gate directly or through no more than 220 ohms to the IO pin.
I know that I connected 2N7777 directly before after web surfing 2N7777 circuits but I can't say 100% now (breadboard disassembled long ago) that IRLZ44N gate direct to pin is safe. I had spent time reading up on those too. Then I wired 220R or direct and it worked.
The FET should switch full ON by 2.0V. I don't see why 1KR between pin and gate should not work but try 220R?